Correct, But the homepage also has a name, Not all homepages are a homepage, Some are the News page, some are something else, etc..

Perhaps, but that's where a theme mod or plugin should come into play. A is_front_page() stuck in the <title> or whatever. Infact one of my sites is like that.

However when you're at http://yoursite.com/, I think the majority of people expect the <title> to be what they've entered at Settings -> General, regardless of what is shown there (latest posts or a welcome message).